\documentclass{beamer}

% \documentclass[handout]{beamer}
% \usepackage{pdfpages}
% \usepackage{handoutWithNotes}
% \pgfpagesuselayout{2 on 1}[a4paper, border shrink=5mm]

%\documentclass[tikz,border=10pt]{standalone}
\usepackage{lmodern}
\usepackage{tikz}

\usepackage{mathtools}

\usepackage{url}
\usepackage{tikz}
\usepackage{amsmath}
\usepackage{hyperref}
\usepackage{listings}
\usepackage{graphicx}

\usepackage{caption}
\usepackage{subcaption}

\include{file/filecontents}

% perche' utilizzato in due sezioni
\input{../figure/slides/figures.tex}

% \usepackage[font=small,skip=1pt]{caption}

\usetikzlibrary{arrows, patterns, calc, decorations.pathreplacing, shapes}
\usefonttheme[onlymath]{serif}

\usetheme[secheader]{Boadilla}
\usecolortheme{beaver}
\useoutertheme[left]{sidebar}

\setbeamercolor{section in sidebar}{fg=black}

\DeclarePairedDelimiter\ceil{\lceil}{\rceil}
\DeclarePairedDelimiter\floor{\lfloor}{\rfloor}

\setbeamercovered{dynamic}

\begin{document}

\title[MrsP]{Multiprocessor resource sharing Protocol}
\subtitle{Implementation and evaluation}
\author{Sebastiano Catellani}
\date{}
\logo{\includegraphics[width=15mm]{../images/unipd-logo.png}}
\institute[University of Padua]{University of Padua\\
Supervisor: Prof. Tullio Vardanega}

\begin{frame}
\titlepage
\end{frame}

\begin{frame}
\frametitle{Overview}
\tableofcontents
\end{frame}

% \include{01_Model}
\include{02_MrsP}
\include{03_Solution}
\include{04_LITMUS}
\include{05_implementation}
\include{06_experiments}
% \include{07_conclusion}

% \begin{frame}
%         \frametitle{References}

%         \fontsize{7pt}{7.2}\selectfont

%         \bibliographystyle{plain}
%     \bibliography{../reference} 
% \end{frame}




% \begin{block}{Problemi aperti}
% Un numero pari $>2$ è sempre la somma di due primi?
% \end{block}
% \begin{exampleblock}{Un esempio}
% $2$ è un numero primo
% \end{exampleblock}
% \begin{alertblock}{Un errore}
% $0=1$
% \end{alertblock}












% \item generalizes uniprocessor RTA: $R_i = C_i + B_i + I_i$
%   \begin{itemize}
%     \item $I_i = \sum\limits_{\tau_j \in hp(i)} \ceil{\frac{R_i}{T_j}} C_j$
%     \item $B_i = max$\{\textcolor{red}{$\hat{c}$}$,\hat{b}\}$
%     \item $C_i = WCET_i + \sum\limits_{r^j \in F(\tau_i)} n_i \textcolor{red}{c^j}$
%   \end{itemize} 



% \begin{frame}
% \frametitle{MrsP}
% \emph{Multiprocessor resource sharing Protocol}
% \begin{itemize}
% \item for partitioned algorithms
% \item spinning-based protocol
% \item generalizes uniprocessor RTA: $R_i = C_i + B_i + I_i$
%   \begin{itemize}
%     \item $I_i = \sum\limits_{\tau_j \in hp(i)} \ceil{\frac{R_i}{T_j}} C_j$
%     \item $B_i = max$\{\textcolor{red}{$\hat{c}$}$,\hat{b}\}$
%     \item $C_i = WCET_i + \sum\limits_{r^j \in F(\tau_i)} n_i \textcolor{red}{c^j}$
%   \end{itemize} 
% \item helping mechanism
% \end{itemize}
% \end{frame}

% \begin{frame}
%   \frametitle{Overheads}

%   Resource lock:\\
%   \begin{itemize}
%     \item change priority, add job to the queue, set ceiling - 800k ns (O(m))
%     \item wake up the queued lock holder - 6k ns (migration)
%     \item busy wait - 400 ns
%   \end{itemize}

%   Resource release:
%   \begin{itemize}
%     \item restore priority, pop job from the queue, restore ceiling - 500 ns
%     \item wake up the queued lock holder - 6k ns (migration)
%     \item Running job migration - 800k ns
%   \end{itemize}

% \end{frame}

% \begin{frame}
%   \frametitle{Overheads}

%   Post context switch 1:
%   \begin{itemize}
%     \item find a new cpu for the preempted lock holder and set up the - migration 24k ns (lock cpu + lock resource)
%     \item perform the migration of the preempted job - 37k ns
%   \end{itemize}

%   Post context switch 2:
%   \begin{itemize}
%     \item a cpu is again available for a migration - 3k ns
%     \item performs the migration of the queued job - 6k ns
%   \end{itemize}  

% \end{frame}

% \begin{frame}
% \frametitle{MrsP}
% %\MrsP{1.5}{1.1}{1.1}
% \centerline{\MrsP{1}{1}}
% \end{frame}

% \begin{frame}

%   \frametitle{Response time - 1}

%   \begin{table}
%   \centering
%   \begin{tabular}{ccccc}
%   \hline\hline
%     Task & Partition     & Priority & Critical section & WCET  \\ \hline
%     $\tau_1$ & $P_1$  & 20 & 1 & 1 \\
%     $\tau_2$ & $P_2$  & 20 & 1 & 1 \\
%     \hline
%     \end{tabular}
%   \end{table}

%   \begin{table}
%   \centering
%   \begin{tabular}{cccc}
%   \hline\hline
%     Task & MrsP & Ceiling & Non preemption \\ \hline
%     $\tau_1$ & 1.123.127 & 1.045.957 & 1.181.310 \\
%     $\tau_2$ & 2.231.823 & 2.029.249 & 2.446.051 \\
%     \hline
%     \end{tabular}
%   \end{table}

% \end{frame}

% \begin{frame}

%   \frametitle{Response time - 2}

%   \begin{table}
%   \centering
%   \begin{tabular}{ccccc}
%   \hline\hline
%     Task & Partition     & Priority & Critical section & WCET  \\ \hline
%     $\tau_1$ & $P_1$  & 20 & 3 & 3 \\
%     $\tau_2$ & $P_2$  & 20 & 3 & 3 \\
%     \hline
%     \end{tabular}
%   \end{table}

%   \begin{table}
%   \centering
%   \begin{tabular}{cccc}
%   \hline\hline
%     Task & MrsP & Ceiling & Non preemption \\ \hline
%     $\tau_1$ & 3.050.809 & 3.145.418 & 3.057.504 \\
%     $\tau_2$ & 5.994.789 & 6.211.880 & 6.067.983 \\
%     \hline
%     \end{tabular}
%   \end{table}

% \end{frame}

% \begin{frame}

%   \frametitle{Response time - 3}

%   \begin{table}
%   \centering
%   \begin{tabular}{ccccc}
%   \hline\hline
%     Task & Partition     & Priority & Critical section & WCET  \\ \hline
%     $\tau_1$ & $P_1$  & 20 & 1 & 1 \\
%     $\tau_2$ & $P_1$  & 10 & 0 & 1 \\
%     $\tau_3$ & $P_2$  & 20 & 1 & 1 \\
%     \hline
%     \end{tabular}
%   \end{table}

%   \begin{table}
%   \centering
%   \begin{tabular}{cccc}
%   \hline\hline
%     Task & MrsP & Ceiling & Non preemption \\ \hline
%     $\tau_1$ & \underline{1.206.362} & 2.194.042 & \underline{1.111.517} \\
%     $\tau_2$ & 1.098.587 & 1.068.602 & 1.977.039 \\
%     $\tau_3$ & 2.351.562 & 3.168.240 & 1.911.890 \\
%     \hline
%     \end{tabular}
%   \end{table}

% \end{frame}

% \begin{frame}

%   \frametitle{Response time - 4}

%   \begin{table}
%   \centering
%   \begin{tabular}{ccccc}
%   \hline\hline
%     Task & Partition     & Priority & Critical section & WCET  \\ \hline
%     $\tau_1$ & $P_1$  & 20 & 3 & 3 \\
%     $\tau_2$ & $P_1$  & 10 & 0 & 1 \\
%     $\tau_3$ & $P_2$  & 20 & 3 & 3 \\
%     \hline
%     \end{tabular}
%   \end{table}

%   \begin{table}
%   \centering
%   \begin{tabular}{cccc}
%   \hline\hline
%     Task & MrsP & Ceiling & Non preemption \\ \hline
%     $\tau_1$ & \underline{3.066.828} & 4.242.092 & \underline{3.177.307} \\
%     $\tau_2$ & 1.035.721 & 1.141.324 & 3.956.506 \\
%     $\tau_3$ & 6.099.752 & 7.209.873 & 6.024.691 \\
%     \hline
%     \end{tabular}
%   \end{table}
% \end{frame}

% \begin{frame}
%   \frametitle{Response time - 5}

%   \begin{table}
%   \centering
%   \begin{tabular}{ccccc}
%   \hline\hline
%     Task & Partition     & Priority & Critical section & WCET  \\ \hline
%     $\tau_1$ & $P_1$  & 20 & 1 & 1 \\
%     $\tau_2$ & $P_1$  & 10 & 0 & 3 \\
%     $\tau_3$ & $P_2$  & 20 & 1 & 1 \\
%     \hline
%     \end{tabular}
%   \end{table}

%   \begin{table}
%   \centering
%   \begin{tabular}{cccc}
%   \hline\hline
%     Task & MrsP & Ceiling & Non preemption \\ \hline
%     $\tau_1$ & \underline{1.053.232} & 4.215.599 & \underline{1.113.397} \\
%     $\tau_2$ & 3.018.344 & 3.071.190 & 4.006.309 \\
%     $\tau_3$ & 2.042.122 & 5.169.139 & 2.068.905 \\
%     \hline
%     \end{tabular}
%   \end{table}

% \end{frame}

% \begin{frame}
% \frametitle{Response time - 6}
%   \begin{table}
%   \centering
%   \begin{tabular}{ccccc}
%   \hline\hline
%     Task & Partition     & Priority & Critical section & WCET  \\ \hline
%     $\tau_1$ & $P_1$  & 20 & 1 & 1 \\
%     $\tau_2$ & $P_1$  & 10 & 0 & 3 \\
%     $\tau_3$ & $P_2$  & 20 & 1 & 1 \\
%     $\tau_4$ & $P_2$  & 10 & 0 & 3 \\
%     $\tau_5$ & $P_3$  & 20 & 1 & 1 \\
%     \hline
%     \end{tabular}
%   \end{table}

%   \begin{table}
%   \centering
%   \begin{tabular}{cccc}
%   \hline\hline
%     Task & MrsP & Ceiling & Non preemption \\ \hline
%     $\tau_1$ & \underline{1.111.410} & 4.312.490 & \underline{1.173.600} \\
%     $\tau_2$ & 3.029.214 & 3.131.630 & 4.205.578 \\
%     $\tau_3$ & \underline{2.062.770} & 5.301.240 & \underline{2.211.347} \\
%     $\tau_4$ & 3.022.036 & 3.099.090 & 5.078.436 \\
%     $\tau_5$ & 3.030.634 & 6.309.370 & 3.184.333 \\
%     \hline
%     \end{tabular}
%   \end{table}

% \end{frame}

\end{document}
